Need help on my understanding of gravitational waves

Hi, Guys. So i am doing a research paper on gravitational waves. As I read through review articles on gravitational waves and LIGO, I don't quite get a few points. The materials are really dense and I don't have the math and physics level to back it up. But I am really interested in the topic.

1) So first of all, I think one article is saying that gravitational waves have this quadrupole moment which allows it to occur. But how does quadrupole moment plays a part in binary star systems such as the neutron stars spin down. What is the connection? I can see energy loses in the system is being emitted as gravitational waves.

2) "LIGO should be able to detect gravitational waves as small as h \approx 5\times 10^{-22}"(WIKI) Using the h strength of gws equation, we approximate the magnitude of the gws to be detected in galaxy. But where in the galaxy? What is the hubble distance? I know this h equation approximates the order of accuracy in LIGO. But how did it come about?

3) Why GWs are detected in amplitude instead of frequency? Aren't we detecting gws base on the strength(as in magnitude of energy) of it.

4)How do we know if we pick up the GWs signal? This is very ambiguous. One article i read said they derived equation to come up with the GWs signal in form of radio-wave. I know they detect the waves in the photodiode where the two beams in LIGO are measured to see if they are out of phrase.

1) So first of all, I think one article is saying that gravitational waves have this quadrupole moment which allows it to occur. But how does quadrupole moment plays a part in binary star systems such as the neutron stars spin down. What is the connection? I can see energy loses in the system is being emitted as gravitational waves.

What is meant is that gravitational radiation is emitted by changes in the quadrupole moment of a mass distribution, NOT the dipole moment as is the case in the electromagnetic case. This means that if you have, for example, a spherical star pulsating radially that it will not radiate gravitational waves! On the other hand, two orbiting bodies produce a changing quadrupole moment.

2) "LIGO should be able to detect gravitational waves as small as h \approx 5\times 10^{-22}"(WIKI) Using the h strength of gws equation, we approximate the magnitude of the gws to be detected in galaxy. But where in the galaxy? What is the hubble distance? I know this h equation approximates the order of accuracy in LIGO. But how did it come about?

3) Why GWs are detected in amplitude instead of frequency? Aren't we detecting gws base on the strength(as in magnitude of energy) of it.

Because the GW changes the length of the arms of the interferometer, which is an effect proportional to the amplitude of the wave. The frequency just tells you how often it's doing this. The energy in the wave is actually irrelevant for LIGO's purposes (it's not like in EM where photons have energy hbar*omega, and that's the relevant quantity. Rather, if you think of looking at a test charge as an electromagnetic wave passes by, the E-field will cause the charge to oscillate with a magnitude equal to the amplitude of the EM wave, and the same frequency as well.)

4)How do we know if we pick up the GWs signal? This is very ambiguous. One article i read said they derived equation to come up with the GWs signal in form of radio-wave. I know they detect the waves in the photodiode where the two beams in LIGO are measured to see if they are out of phrase.

What do you mean? You measure the distance in the two arms of the interferometer. If you see this distance changing by larger amounts than your noise threshold, that's a signal. If it has the right frequency characteristics, then it's possibly a GW of astrophysical origin (other things are of course possible, like falling trees nearby or construction equipment). The characteristic 'chirp' of a binary inspiral is actually an unmistakable signal, you can hear it here: http://www.einstein-online.info/spotlights/chirping_neutron_stars ).